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Simplifying 36n2 + 48np + 16p2 = 0 Reorder the terms: 48np + 36n2 + 16p2 = 0 Solving 48np + 36n2 + 16p2 = 0 Solving for variable 'n'. Factor out the Greatest Common Factor (GCF), '4'. 4(12np + 9n2 + 4p2) = 0 Factor a trinomial. 4((3n + 2p)(3n + 2p)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(3n + 2p)' equal to zero and attempt to solve: Simplifying 3n + 2p = 0 Solving 3n + 2p = 0 Move all terms containing n to the left, all other terms to the right. Add '-2p' to each side of the equation. 3n + 2p + -2p = 0 + -2p Combine like terms: 2p + -2p = 0 3n + 0 = 0 + -2p 3n = 0 + -2p Remove the zero: 3n = -2p Divide each side by '3'. n = -0.6666666667p Simplifying n = -0.6666666667pSubproblem 2
Set the factor '(3n + 2p)' equal to zero and attempt to solve: Simplifying 3n + 2p = 0 Solving 3n + 2p = 0 Move all terms containing n to the left, all other terms to the right. Add '-2p' to each side of the equation. 3n + 2p + -2p = 0 + -2p Combine like terms: 2p + -2p = 0 3n + 0 = 0 + -2p 3n = 0 + -2p Remove the zero: 3n = -2p Divide each side by '3'. n = -0.6666666667p Simplifying n = -0.6666666667pSolution
n = {-0.6666666667p, -0.6666666667p}
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